The paper deals with the detuning optimization of a mistuned bladed-disk in presence of geometrical nonlinearities. A full data basis is constructed by using a finite element model of a bladed-disk with cyclic order 12, which allows all the possible detuning configurations to be computed. It is then proposed to reformulate the combinatorial optimization problem in a probabilistic framework, using and adapting the recent Probabilistic Learning on Manifolds (PLoM) tool to the detuning context. The available full data basis is used in order to validate the proposed method.